This app aims to replace Google Reader as it is being shut down. It's entirely based on Tiny Tiny RSS reader, so all thanks goes to Andrew Dolgov.
As I said, you will get almost what you could do with GReader : there's the web version on https://tt-rss.dedikewl.fr/. Go there and create an account. Then download this app and put your login/password, and now you can read your feeds both on your desktop computer with the web version and on all your android devices with this app. They all get synchronized. And the android app support offline mode with image downloading.
Feel free to email me if you have any questions.
PS : you need to enable API access in your account preferences on the website after login in for the first time or the android won't work.
Source code : https://github.com/redam/dedittrss
Licensed under GNU GPL version 2.
Original source code: https://github.com/gothfox/Tiny-Tiny-RSS-for-Honeycomb